The average weight of two football players P and Q is 38 kg. The average weight of P, Q and their coach T is 49 kg. What is the weight of the coach in kilograms?

Introduction / Context:
This problem is a simple application of averages with a small group. You are given the average weight of two players and then the average weight when their coach is also included. Using these two pieces of information, you must determine the coach weight. This style of question is frequently seen in school level aptitude tests and entrance exams.

Given Data / Assumptions:
- Players P and Q have an average weight of 38 kg.
- The average weight of P and Q together is 38 kg, so their combined weight is 2 * 38 kg.
- When coach T is included with P and Q, the new average becomes 49 kg for the three persons.
- We must find the coach T weight in kilograms.

Concept / Approach:
The key idea is again that average multiplied by the number of people gives the total weight. First, calculate the combined weight of P and Q from their average. Next, compute the combined weight of P, Q and T from the new average. The difference between these two totals must be the coach weight. This is a simple and reliable technique for small group average problems.

Step-by-Step Solution:
Step 1: Average weight of P and Q is 38 kg.Step 2: Total weight of P and Q together = 2 * 38 = 76 kg.Step 3: When coach T joins, there are 3 persons (P, Q and T) with average weight 49 kg.Step 4: Total weight of P, Q and T = 3 * 49 = 147 kg.Step 5: Coach weight T = total of three persons minus total of players P and Q.Step 6: T = 147 - 76 = 71 kg.Step 7: Therefore, the coach weight is 71 kg.

Verification / Alternative check:
If P and Q together weigh 76 kg and the coach weighs 71 kg, then the total for all three is 76 + 71 = 147 kg. The average for three persons is 147 / 3 = 49 kg, which matches the given average. The original average of P and Q alone is 76 / 2 = 38 kg, which also matches the problem statement. This confirms that the calculation is consistent and correct.

Why Other Options Are Wrong:
Values such as 46 kg, 76 kg or 91 kg do not produce a total of 147 kg when added to 76 kg, and so they do not yield an average of 49 kg for three persons. A quick recomputation of total and average with these alternative values will show that the resulting averages are not 49 kg. Hence they cannot be correct.

Common Pitfalls:
Students sometimes confuse whether the average is given for two persons or three persons, or they mistakenly divide by 2 instead of 3 when computing the new average. Another pitfall is to think that the coach weight is simply 49 - 38, ignoring the effect of the number of persons. Always convert averages to total sums and work with those totals to avoid such errors.

Final Answer:
The coach weight is 71 kg.